Question

if area of semicircle is 154 cm
$area \: = 154cm ^{2}$
. Find it's Diameter​

Answer 1

Question :–

• Area of semi circle is 154 cm² , then find Diameter of circle .

ANSWER :–

GIVEN :–

• Area of semi circle = 154 cm²

TO FIND :–

• Diameter of circle = ?

SOLUTION :–

$\\ \longrightarrow{ \bold{Area \: \: of \: \: circle \: = \pi {r}^{2} }}$

$\\ \longrightarrow{ \bold{Area \: \: of \: \: Semi \: \: circle \: = \dfrac{1}{2} \pi {r}^{2} }}$

• According to the question –

$\\ \implies{ \bold{Area \: \: of \: \: Semi \: \: circle \: = 154}}$

$\\ \implies{ \bold{\dfrac{1}{2} \pi {r}^{2} = 154}}$

$\\ \implies{ \bold{ \pi {r}^{2} = 154 \times 2}}$

$\\ \implies{ \bold{ \dfrac{22}{7} {r}^{2} = 308}}$

$\\ \implies{ \bold{ {r}^{2} = 308 \times \dfrac{7}{22} }}$

$\\ \implies{ \bold{ {r}^{2} = 98 }}$

$\\ \implies{ \bold{ {r}^{} = \sqrt{ 98} }}$

▪︎ And –

$\\ \longrightarrow{ \bold{ Diameter = 2r}}$

$\\ \implies{ \bold{ Diameter = 2( \sqrt{98}) }}$

$\\ \implies{ \bold{ Diameter = 2 \sqrt{2 \times 49} }}$

$\\ \large \to \: { \boxed{ \bold{ Diameter = 14 \sqrt{2 } \: cm}}}$

Answer 2

✯✯ QUESTION ✯✯

If Area of Semicircle is 154 cm.Find it's Diameter ...

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✰✰ ANSWER ✰✰

$\longmapsto\tt{Area\:of\:Circle=\pi{{r}^{2}}}$

$\longmapsto\tt{Area\:of\:semi-circle=\dfrac{1}{2}\pi{{r}^{2}}}$

➥Putting Values : -

$\longmapsto\tt{154=\dfrac{1}{\cancel{2}}\times\dfrac{\cancel{22}}{7}\times{{r}^{2}}}$

$\longmapsto\tt{154=\dfrac{11{r}^{2}}{7}}$

$\longmapsto\tt{{r}^{2}=\dfrac{\cancel{154}\times{7}}{\cancel{11}}}$

$\longmapsto\tt{{r}^{2}=14\times{7}}$

$\longmapsto\tt{{r}^{2}=\sqrt{98}}$

➥Now ,

As we know that diameter is double of radius .So ,

$\longmapsto\tt{Diameter=2r}$

$\longmapsto\tt{2\sqrt{(98)}}$

$\longmapsto\tt{2\sqrt{2\times{49}}}$

$\pink\longmapsto\:\large\underline{\boxed{\bf\red{Diameter}\blue{=}\orange{14\sqrt{2}cm.}}}$